Férmions relativísticos sem massa confinados à Fita de Moebius

Abstract

In this paper, we investigate the theoretical effects of the curvature of the Möbius strip on the quantum dynamics of massless relativistic fermions confined to this surface, starting from the solution of the Dirac equation. We work on the approximation that at low energies the particle exhibits a linear dispersion relation and obeys the relativistic wave equation. The curvature induces a geometric effective potential when the particle performs a loop around the strip. We study how the potential modifies the eigenfunctions and energy levels, obtained through a WKB approximation, by analyzing the regions of wells and barriers generated by the curvature. The energy spectrum is estimated by fixing the value of the parameters describing the ribbon, resulting in a movement along wires and rings.